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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "# FOURIER SINE SERIE
S OF A SQUARE WAVE" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "# f(x) = 1 on (0,Pi); f(x) =
 -1 on (-Pi,0); f has period 2*Pi." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "# First
 we need to calculate the Fourier coefficients." }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 36 "bn := (2/Pi)*Int(sin(n*x), x=0..Pi);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(%);" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 28 "# This is 0 unless n is odd." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 94 "# Note that, unlike the coefficients of the triangle \+
wave, these decrease like 1/n, not 1/n^2." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "bodd \+
:= k -> (4/Pi)*(1/(2*k+1));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
55 "partialsum := K -> sum(bodd(k)*sin((2*k+1)*x), k=0..K);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(partialsum(0), x=-8..8)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(partialsum(1), x=
-8..8);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(partialsum(
2), x=-8..8);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(parti
alsum(4), x=-8..8);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot
(partialsum(8), x=-8..8);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
30 "plot(partialsum(16), x=-8..8);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "# Let's look up close." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "plot(partialsum(16), x=-1..4);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 30 "plot(partialsum(32), x=-1..4);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot(partialsum(64), x=-1..4);" }}}
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